"Why is it only the US who seem to have a crime of Home Invasion? "
That's odd. They happen in lots of countries.
When someone comes into your house armed, intentionally while you are there, takes you captive, and does various crimijnal things with or without hurting you or compelling you to assist them in criminal acts, that is a 'home invasion'.
If you are not there, it's just burglary, unless they burn the house down, when it becomes 'and arson'.